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In this paper, a promising spectrum sensing technique is proposed using Neyman Pearson (NP) based energy detection scheme for cognitive radio (CR) systems, where the secondary user is running in full duplex (FD) mode under residual self-interference (SI). First, NP based likelihood ratio test is carried out in additive white Gaussian noise (AWGN) environment and the closed form expressions for performance metrics are derived analytically. Next, minimum mean square error based estimator correlator for spectrum sensing under AWGN scenario is proposed, where PU signal having uncertain/arbitrary covariance structure is considered affirming a more realistic scenario in a heterogeneous network. Finally, the proposed detection scheme is extended to a practical Rayleigh fading scenario in FD CR under residual SI, where closed form analytical expressions for performance metrics are also derived. The …